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## Compute in a quotient of a polynomial ring

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.16 Solution: (1) Evidently, $$\overline{g(x)} = \overline{-2x^3 + 25936x + 3}.$$ (2) Note that $$x^4-16 = (x+2)(x-2)(x^2+4).$$…

## Compute the kernel of a coordinate projection

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.6 Exercise 1.6.15 Define a map $\pi : \mathbb{R}^2 \rightarrow \mathbb{R}$ by $\pi((x,y)) = x$. Prove that $\pi$ is…